/*
   Include "petsctao.h" so that we can use TAO solvers.  Note that this
   file automatically includes libraries such as:
     petsc.h       - base PETSc routines   petscvec.h - vectors
     petscsys.h    - system routines        petscmat.h - matrices
     petscis.h     - index sets            petscksp.h - Krylov subspace methods
     petscviewer.h - viewers               petscpc.h  - preconditioners

 This version tests correlated terms using both vector and listed forms
*/

#include <petsctao.h>

/*
Description:   These data are the result of a NIST study involving
               ultrasonic calibration.  The response variable is
               ultrasonic response, and the predictor variable is
               metal distance.

Reference:     Chwirut, D., NIST (197?).
               Ultrasonic Reference Block Study.
*/

static char help[] = "Finds the nonlinear least-squares solution to the model \n\
            y = exp[-b1*x]/(b2+b3*x)  +  e \n";

#define NOBSERVATIONS 214
#define NPARAMETERS   3

/* User-defined application context */
typedef struct {
  /* Working space */
  PetscReal t[NOBSERVATIONS];              /* array of independent variables of observation */
  PetscReal y[NOBSERVATIONS];              /* array of dependent variables */
  PetscReal j[NOBSERVATIONS][NPARAMETERS]; /* dense jacobian matrix array*/
  PetscInt  idm[NOBSERVATIONS];            /* Matrix indices for jacobian */
  PetscInt  idn[NPARAMETERS];
} AppCtx;

/* User provided Routines */
PetscErrorCode InitializeData(AppCtx *user);
PetscErrorCode FormStartingPoint(Vec);
PetscErrorCode EvaluateFunction(Tao, Vec, Vec, void *);
PetscErrorCode EvaluateJacobian(Tao, Vec, Mat, Mat, void *);

/*--------------------------------------------------------------------*/
int main(int argc, char **argv)
{
  PetscInt  wtype = 0;
  Vec       x, f; /* solution, function */
  Vec       w;    /* weights */
  Mat       J;    /* Jacobian matrix */
  Tao       tao;  /* Tao solver context */
  PetscInt  i;    /* iteration information */
  PetscReal hist[100], resid[100];
  PetscInt  lits[100];
  PetscInt  w_row[NOBSERVATIONS]; /* explicit weights */
  PetscInt  w_col[NOBSERVATIONS];
  PetscReal w_vals[NOBSERVATIONS];
  PetscBool flg;
  AppCtx    user; /* user-defined work context */

  PetscFunctionBeginUser;
  PetscCall(PetscInitialize(&argc, &argv, (char *)0, help));
  PetscCall(PetscOptionsGetInt(NULL, NULL, "-wtype", &wtype, &flg));
  PetscCall(PetscPrintf(PETSC_COMM_WORLD, "wtype=%" PetscInt_FMT "\n", wtype));
  /* Allocate vectors */
  PetscCall(VecCreateSeq(MPI_COMM_SELF, NPARAMETERS, &x));
  PetscCall(VecCreateSeq(MPI_COMM_SELF, NOBSERVATIONS, &f));

  PetscCall(VecDuplicate(f, &w));

  /* no correlation, but set in different ways */
  PetscCall(VecSet(w, 1.0));
  for (i = 0; i < NOBSERVATIONS; i++) {
    w_row[i]  = i;
    w_col[i]  = i;
    w_vals[i] = 1.0;
  }

  /* Create the Jacobian matrix. */
  PetscCall(MatCreateSeqDense(MPI_COMM_SELF, NOBSERVATIONS, NPARAMETERS, NULL, &J));

  for (i = 0; i < NOBSERVATIONS; i++) user.idm[i] = i;

  for (i = 0; i < NPARAMETERS; i++) user.idn[i] = i;

  /* Create TAO solver and set desired solution method */
  PetscCall(TaoCreate(PETSC_COMM_SELF, &tao));
  PetscCall(TaoSetType(tao, TAOPOUNDERS));

  /* Set the function and Jacobian routines. */
  PetscCall(InitializeData(&user));
  PetscCall(FormStartingPoint(x));
  PetscCall(TaoSetSolution(tao, x));
  PetscCall(TaoSetResidualRoutine(tao, f, EvaluateFunction, (void *)&user));
  if (wtype == 1) {
    PetscCall(TaoSetResidualWeights(tao, w, 0, NULL, NULL, NULL));
  } else if (wtype == 2) {
    PetscCall(TaoSetResidualWeights(tao, NULL, NOBSERVATIONS, w_row, w_col, w_vals));
  }
  PetscCall(TaoSetJacobianResidualRoutine(tao, J, J, EvaluateJacobian, (void *)&user));
  PetscCall(TaoSetTolerances(tao, 1e-5, 0.0, PETSC_DEFAULT));

  /* Check for any TAO command line arguments */
  PetscCall(TaoSetFromOptions(tao));

  PetscCall(TaoSetConvergenceHistory(tao, hist, resid, 0, lits, 100, PETSC_TRUE));
  /* Perform the Solve */
  PetscCall(TaoSolve(tao));

  /* Free TAO data structures */
  PetscCall(TaoDestroy(&tao));

  /* Free PETSc data structures */
  PetscCall(VecDestroy(&x));
  PetscCall(VecDestroy(&w));
  PetscCall(VecDestroy(&f));
  PetscCall(MatDestroy(&J));

  PetscCall(PetscFinalize());
  return 0;
}

/*--------------------------------------------------------------------*/
PetscErrorCode EvaluateFunction(Tao tao, Vec X, Vec F, void *ptr)
{
  AppCtx          *user = (AppCtx *)ptr;
  PetscInt         i;
  PetscReal       *y = user->y, *f, *t = user->t;
  const PetscReal *x;

  PetscFunctionBegin;
  PetscCall(VecGetArrayRead(X, &x));
  PetscCall(VecGetArray(F, &f));

  for (i = 0; i < NOBSERVATIONS; i++) f[i] = y[i] - PetscExpScalar(-x[0] * t[i]) / (x[1] + x[2] * t[i]);
  PetscCall(VecRestoreArrayRead(X, &x));
  PetscCall(VecRestoreArray(F, &f));
  PetscCall(PetscLogFlops(6 * NOBSERVATIONS));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*------------------------------------------------------------*/
/* J[i][j] = df[i]/dt[j] */
PetscErrorCode EvaluateJacobian(Tao tao, Vec X, Mat J, Mat Jpre, void *ptr)
{
  AppCtx          *user = (AppCtx *)ptr;
  PetscInt         i;
  PetscReal       *t = user->t;
  const PetscReal *x;
  PetscReal        base;

  PetscFunctionBegin;
  PetscCall(VecGetArrayRead(X, &x));
  for (i = 0; i < NOBSERVATIONS; i++) {
    base = PetscExpScalar(-x[0] * t[i]) / (x[1] + x[2] * t[i]);

    user->j[i][0] = t[i] * base;
    user->j[i][1] = base / (x[1] + x[2] * t[i]);
    user->j[i][2] = base * t[i] / (x[1] + x[2] * t[i]);
  }

  /* Assemble the matrix */
  PetscCall(MatSetValues(J, NOBSERVATIONS, user->idm, NPARAMETERS, user->idn, (PetscReal *)user->j, INSERT_VALUES));
  PetscCall(MatAssemblyBegin(J, MAT_FINAL_ASSEMBLY));
  PetscCall(MatAssemblyEnd(J, MAT_FINAL_ASSEMBLY));

  PetscCall(VecRestoreArrayRead(X, &x));
  PetscCall(PetscLogFlops(NOBSERVATIONS * 13));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/* ------------------------------------------------------------ */
PetscErrorCode FormStartingPoint(Vec X)
{
  PetscReal *x;

  PetscFunctionBegin;
  PetscCall(VecGetArray(X, &x));
  x[0] = 1.19;
  x[1] = -1.86;
  x[2] = 1.08;
  PetscCall(VecRestoreArray(X, &x));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/* ---------------------------------------------------------------------- */
PetscErrorCode InitializeData(AppCtx *user)
{
  PetscReal *t = user->t, *y = user->y;
  PetscInt   i = 0;

  PetscFunctionBegin;
  y[i]   = 92.9000;
  t[i++] = 0.5000;
  y[i]   = 78.7000;
  t[i++] = 0.6250;
  y[i]   = 64.2000;
  t[i++] = 0.7500;
  y[i]   = 64.9000;
  t[i++] = 0.8750;
  y[i]   = 57.1000;
  t[i++] = 1.0000;
  y[i]   = 43.3000;
  t[i++] = 1.2500;
  y[i]   = 31.1000;
  t[i++] = 1.7500;
  y[i]   = 23.6000;
  t[i++] = 2.2500;
  y[i]   = 31.0500;
  t[i++] = 1.7500;
  y[i]   = 23.7750;
  t[i++] = 2.2500;
  y[i]   = 17.7375;
  t[i++] = 2.7500;
  y[i]   = 13.8000;
  t[i++] = 3.2500;
  y[i]   = 11.5875;
  t[i++] = 3.7500;
  y[i]   = 9.4125;
  t[i++] = 4.2500;
  y[i]   = 7.7250;
  t[i++] = 4.7500;
  y[i]   = 7.3500;
  t[i++] = 5.2500;
  y[i]   = 8.0250;
  t[i++] = 5.7500;
  y[i]   = 90.6000;
  t[i++] = 0.5000;
  y[i]   = 76.9000;
  t[i++] = 0.6250;
  y[i]   = 71.6000;
  t[i++] = 0.7500;
  y[i]   = 63.6000;
  t[i++] = 0.8750;
  y[i]   = 54.0000;
  t[i++] = 1.0000;
  y[i]   = 39.2000;
  t[i++] = 1.2500;
  y[i]   = 29.3000;
  t[i++] = 1.7500;
  y[i]   = 21.4000;
  t[i++] = 2.2500;
  y[i]   = 29.1750;
  t[i++] = 1.7500;
  y[i]   = 22.1250;
  t[i++] = 2.2500;
  y[i]   = 17.5125;
  t[i++] = 2.7500;
  y[i]   = 14.2500;
  t[i++] = 3.2500;
  y[i]   = 9.4500;
  t[i++] = 3.7500;
  y[i]   = 9.1500;
  t[i++] = 4.2500;
  y[i]   = 7.9125;
  t[i++] = 4.7500;
  y[i]   = 8.4750;
  t[i++] = 5.2500;
  y[i]   = 6.1125;
  t[i++] = 5.7500;
  y[i]   = 80.0000;
  t[i++] = 0.5000;
  y[i]   = 79.0000;
  t[i++] = 0.6250;
  y[i]   = 63.8000;
  t[i++] = 0.7500;
  y[i]   = 57.2000;
  t[i++] = 0.8750;
  y[i]   = 53.2000;
  t[i++] = 1.0000;
  y[i]   = 42.5000;
  t[i++] = 1.2500;
  y[i]   = 26.8000;
  t[i++] = 1.7500;
  y[i]   = 20.4000;
  t[i++] = 2.2500;
  y[i]   = 26.8500;
  t[i++] = 1.7500;
  y[i]   = 21.0000;
  t[i++] = 2.2500;
  y[i]   = 16.4625;
  t[i++] = 2.7500;
  y[i]   = 12.5250;
  t[i++] = 3.2500;
  y[i]   = 10.5375;
  t[i++] = 3.7500;
  y[i]   = 8.5875;
  t[i++] = 4.2500;
  y[i]   = 7.1250;
  t[i++] = 4.7500;
  y[i]   = 6.1125;
  t[i++] = 5.2500;
  y[i]   = 5.9625;
  t[i++] = 5.7500;
  y[i]   = 74.1000;
  t[i++] = 0.5000;
  y[i]   = 67.3000;
  t[i++] = 0.6250;
  y[i]   = 60.8000;
  t[i++] = 0.7500;
  y[i]   = 55.5000;
  t[i++] = 0.8750;
  y[i]   = 50.3000;
  t[i++] = 1.0000;
  y[i]   = 41.0000;
  t[i++] = 1.2500;
  y[i]   = 29.4000;
  t[i++] = 1.7500;
  y[i]   = 20.4000;
  t[i++] = 2.2500;
  y[i]   = 29.3625;
  t[i++] = 1.7500;
  y[i]   = 21.1500;
  t[i++] = 2.2500;
  y[i]   = 16.7625;
  t[i++] = 2.7500;
  y[i]   = 13.2000;
  t[i++] = 3.2500;
  y[i]   = 10.8750;
  t[i++] = 3.7500;
  y[i]   = 8.1750;
  t[i++] = 4.2500;
  y[i]   = 7.3500;
  t[i++] = 4.7500;
  y[i]   = 5.9625;
  t[i++] = 5.2500;
  y[i]   = 5.6250;
  t[i++] = 5.7500;
  y[i]   = 81.5000;
  t[i++] = .5000;
  y[i]   = 62.4000;
  t[i++] = .7500;
  y[i]   = 32.5000;
  t[i++] = 1.5000;
  y[i]   = 12.4100;
  t[i++] = 3.0000;
  y[i]   = 13.1200;
  t[i++] = 3.0000;
  y[i]   = 15.5600;
  t[i++] = 3.0000;
  y[i]   = 5.6300;
  t[i++] = 6.0000;
  y[i]   = 78.0000;
  t[i++] = .5000;
  y[i]   = 59.9000;
  t[i++] = .7500;
  y[i]   = 33.2000;
  t[i++] = 1.5000;
  y[i]   = 13.8400;
  t[i++] = 3.0000;
  y[i]   = 12.7500;
  t[i++] = 3.0000;
  y[i]   = 14.6200;
  t[i++] = 3.0000;
  y[i]   = 3.9400;
  t[i++] = 6.0000;
  y[i]   = 76.8000;
  t[i++] = .5000;
  y[i]   = 61.0000;
  t[i++] = .7500;
  y[i]   = 32.9000;
  t[i++] = 1.5000;
  y[i]   = 13.8700;
  t[i++] = 3.0000;
  y[i]   = 11.8100;
  t[i++] = 3.0000;
  y[i]   = 13.3100;
  t[i++] = 3.0000;
  y[i]   = 5.4400;
  t[i++] = 6.0000;
  y[i]   = 78.0000;
  t[i++] = .5000;
  y[i]   = 63.5000;
  t[i++] = .7500;
  y[i]   = 33.8000;
  t[i++] = 1.5000;
  y[i]   = 12.5600;
  t[i++] = 3.0000;
  y[i]   = 5.6300;
  t[i++] = 6.0000;
  y[i]   = 12.7500;
  t[i++] = 3.0000;
  y[i]   = 13.1200;
  t[i++] = 3.0000;
  y[i]   = 5.4400;
  t[i++] = 6.0000;
  y[i]   = 76.8000;
  t[i++] = .5000;
  y[i]   = 60.0000;
  t[i++] = .7500;
  y[i]   = 47.8000;
  t[i++] = 1.0000;
  y[i]   = 32.0000;
  t[i++] = 1.5000;
  y[i]   = 22.2000;
  t[i++] = 2.0000;
  y[i]   = 22.5700;
  t[i++] = 2.0000;
  y[i]   = 18.8200;
  t[i++] = 2.5000;
  y[i]   = 13.9500;
  t[i++] = 3.0000;
  y[i]   = 11.2500;
  t[i++] = 4.0000;
  y[i]   = 9.0000;
  t[i++] = 5.0000;
  y[i]   = 6.6700;
  t[i++] = 6.0000;
  y[i]   = 75.8000;
  t[i++] = .5000;
  y[i]   = 62.0000;
  t[i++] = .7500;
  y[i]   = 48.8000;
  t[i++] = 1.0000;
  y[i]   = 35.2000;
  t[i++] = 1.5000;
  y[i]   = 20.0000;
  t[i++] = 2.0000;
  y[i]   = 20.3200;
  t[i++] = 2.0000;
  y[i]   = 19.3100;
  t[i++] = 2.5000;
  y[i]   = 12.7500;
  t[i++] = 3.0000;
  y[i]   = 10.4200;
  t[i++] = 4.0000;
  y[i]   = 7.3100;
  t[i++] = 5.0000;
  y[i]   = 7.4200;
  t[i++] = 6.0000;
  y[i]   = 70.5000;
  t[i++] = .5000;
  y[i]   = 59.5000;
  t[i++] = .7500;
  y[i]   = 48.5000;
  t[i++] = 1.0000;
  y[i]   = 35.8000;
  t[i++] = 1.5000;
  y[i]   = 21.0000;
  t[i++] = 2.0000;
  y[i]   = 21.6700;
  t[i++] = 2.0000;
  y[i]   = 21.0000;
  t[i++] = 2.5000;
  y[i]   = 15.6400;
  t[i++] = 3.0000;
  y[i]   = 8.1700;
  t[i++] = 4.0000;
  y[i]   = 8.5500;
  t[i++] = 5.0000;
  y[i]   = 10.1200;
  t[i++] = 6.0000;
  y[i]   = 78.0000;
  t[i++] = .5000;
  y[i]   = 66.0000;
  t[i++] = .6250;
  y[i]   = 62.0000;
  t[i++] = .7500;
  y[i]   = 58.0000;
  t[i++] = .8750;
  y[i]   = 47.7000;
  t[i++] = 1.0000;
  y[i]   = 37.8000;
  t[i++] = 1.2500;
  y[i]   = 20.2000;
  t[i++] = 2.2500;
  y[i]   = 21.0700;
  t[i++] = 2.2500;
  y[i]   = 13.8700;
  t[i++] = 2.7500;
  y[i]   = 9.6700;
  t[i++] = 3.2500;
  y[i]   = 7.7600;
  t[i++] = 3.7500;
  y[i]   = 5.4400;
  t[i++] = 4.2500;
  y[i]   = 4.8700;
  t[i++] = 4.7500;
  y[i]   = 4.0100;
  t[i++] = 5.2500;
  y[i]   = 3.7500;
  t[i++] = 5.7500;
  y[i]   = 24.1900;
  t[i++] = 3.0000;
  y[i]   = 25.7600;
  t[i++] = 3.0000;
  y[i]   = 18.0700;
  t[i++] = 3.0000;
  y[i]   = 11.8100;
  t[i++] = 3.0000;
  y[i]   = 12.0700;
  t[i++] = 3.0000;
  y[i]   = 16.1200;
  t[i++] = 3.0000;
  y[i]   = 70.8000;
  t[i++] = .5000;
  y[i]   = 54.7000;
  t[i++] = .7500;
  y[i]   = 48.0000;
  t[i++] = 1.0000;
  y[i]   = 39.8000;
  t[i++] = 1.5000;
  y[i]   = 29.8000;
  t[i++] = 2.0000;
  y[i]   = 23.7000;
  t[i++] = 2.5000;
  y[i]   = 29.6200;
  t[i++] = 2.0000;
  y[i]   = 23.8100;
  t[i++] = 2.5000;
  y[i]   = 17.7000;
  t[i++] = 3.0000;
  y[i]   = 11.5500;
  t[i++] = 4.0000;
  y[i]   = 12.0700;
  t[i++] = 5.0000;
  y[i]   = 8.7400;
  t[i++] = 6.0000;
  y[i]   = 80.7000;
  t[i++] = .5000;
  y[i]   = 61.3000;
  t[i++] = .7500;
  y[i]   = 47.5000;
  t[i++] = 1.0000;
  y[i]   = 29.0000;
  t[i++] = 1.5000;
  y[i]   = 24.0000;
  t[i++] = 2.0000;
  y[i]   = 17.7000;
  t[i++] = 2.5000;
  y[i]   = 24.5600;
  t[i++] = 2.0000;
  y[i]   = 18.6700;
  t[i++] = 2.5000;
  y[i]   = 16.2400;
  t[i++] = 3.0000;
  y[i]   = 8.7400;
  t[i++] = 4.0000;
  y[i]   = 7.8700;
  t[i++] = 5.0000;
  y[i]   = 8.5100;
  t[i++] = 6.0000;
  y[i]   = 66.7000;
  t[i++] = .5000;
  y[i]   = 59.2000;
  t[i++] = .7500;
  y[i]   = 40.8000;
  t[i++] = 1.0000;
  y[i]   = 30.7000;
  t[i++] = 1.5000;
  y[i]   = 25.7000;
  t[i++] = 2.0000;
  y[i]   = 16.3000;
  t[i++] = 2.5000;
  y[i]   = 25.9900;
  t[i++] = 2.0000;
  y[i]   = 16.9500;
  t[i++] = 2.5000;
  y[i]   = 13.3500;
  t[i++] = 3.0000;
  y[i]   = 8.6200;
  t[i++] = 4.0000;
  y[i]   = 7.2000;
  t[i++] = 5.0000;
  y[i]   = 6.6400;
  t[i++] = 6.0000;
  y[i]   = 13.6900;
  t[i++] = 3.0000;
  y[i]   = 81.0000;
  t[i++] = .5000;
  y[i]   = 64.5000;
  t[i++] = .7500;
  y[i]   = 35.5000;
  t[i++] = 1.5000;
  y[i]   = 13.3100;
  t[i++] = 3.0000;
  y[i]   = 4.8700;
  t[i++] = 6.0000;
  y[i]   = 12.9400;
  t[i++] = 3.0000;
  y[i]   = 5.0600;
  t[i++] = 6.0000;
  y[i]   = 15.1900;
  t[i++] = 3.0000;
  y[i]   = 14.6200;
  t[i++] = 3.0000;
  y[i]   = 15.6400;
  t[i++] = 3.0000;
  y[i]   = 25.5000;
  t[i++] = 1.7500;
  y[i]   = 25.9500;
  t[i++] = 1.7500;
  y[i]   = 81.7000;
  t[i++] = .5000;
  y[i]   = 61.6000;
  t[i++] = .7500;
  y[i]   = 29.8000;
  t[i++] = 1.7500;
  y[i]   = 29.8100;
  t[i++] = 1.7500;
  y[i]   = 17.1700;
  t[i++] = 2.7500;
  y[i]   = 10.3900;
  t[i++] = 3.7500;
  y[i]   = 28.4000;
  t[i++] = 1.7500;
  y[i]   = 28.6900;
  t[i++] = 1.7500;
  y[i]   = 81.3000;
  t[i++] = .5000;
  y[i]   = 60.9000;
  t[i++] = .7500;
  y[i]   = 16.6500;
  t[i++] = 2.7500;
  y[i]   = 10.0500;
  t[i++] = 3.7500;
  y[i]   = 28.9000;
  t[i++] = 1.7500;
  y[i]   = 28.9500;
  t[i++] = 1.7500;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*TEST

     build:
       requires: !complex

     test:
       args:  -tao_smonitor -tao_max_it 100 -tao_type pounders -tao_pounders_delta 0.05 -tao_gatol 1.e-5
       requires: !single
       TODO: produces different output for many different systems

     test:
       suffix: 2
       args: -tao_smonitor -tao_max_it 100 -wtype 1 -tao_type pounders -tao_pounders_delta 0.05 -tao_gatol 1.e-5
       requires: !single
       TODO: produces different output for many different systems

     test:
       suffix: 3
       args: -tao_smonitor -tao_max_it 100 -wtype 2 -tao_type pounders -tao_pounders_delta 0.05 -tao_gatol 1.e-5
       requires: !single
       TODO: produces different output for many different systems

     test:
       suffix: 4
       args: -tao_smonitor -tao_max_it 100 -tao_type pounders -tao_pounders_delta 0.05 -pounders_subsolver_tao_type blmvm -tao_gatol 1.e-5
       requires: !single
       TODO: produces different output for many different systems

 TEST*/
